have developed an alternative conceptual framework for interaction that is not based on statistical models (Rothman and Greenland, 1998a; Rothman and Greenland, 2005). The logic of this new conceptualization is described in detail in the paper provided in Appendix E by Sharon Schwartz and summarized below; it leads to the conclusion that the additive scale is the only meaningful reference point for the measurement of interaction. Few investigators are aware of this new conceptualization of interaction, and hence few have used it as a basis for interpreting their findings.
From a statistical point of view, interaction can be defined as a deviation from conditional independence, a state in which the effect of one factor (social, behavioral, or genetic) on health is the same within strata defined by another factor. This definition implies that an interaction is present if the effect of a social or behavioral factor on disease risk differs among individuals with different genotypes, or if the effect of a genotype on disease risk differs among individuals with different levels of a social or behavioral factor. The problem with this definition, as indicated above, is that it is entirely dependent on the measurement scale (multiplicative or additive). Ratio measures such as relative risks (RRs) or odds ratios (ORs) assess the effects of risk factors on a multiplicative scale, because they reflect the degree to which disease risk (for RR) or odds (for OR) are multiplied in individuals with the risk factor compared to those without. In contrast, risk differences (RD) assess the effects of risk factors on an additive scale, because they reflect how much disease risk is added in individuals who have the risk factor, compared with those who do not. The statistical definition of interaction differs depending on which of these measurement scales is used. For example, in the consideration of factors A and B, interaction on a multiplicative scale is defined as a different RR for factor A across strata defined by factor B, while on an additive scale, interaction is defined as a different RD for factor A across strata defined by factor B. Use of these two different measurement scales can lead to substantively different conclusions in studies of interaction.
Table 8-1 illustrates the relationship, in general, between interaction defined on the multiplicative and additive scales. The risks to four categories of individuals are considered: those who have both a risk-influencing genotype and an environmental exposure (r11), the genotype but not the exposure (r01), the exposure but not the genotype (r10), and neither (r00). On the multiplicative scale, interaction is defined by (r11/r01) ≠ (r10/r00), while on the additive scale it is defined by (r11−r01) ≠ (r10−r00). To facilitate comparison of these two measures, it is convenient to express both as RRs, with the risk in individuals with neither genotype nor exposure as the